You may also like

Compactness and Contradiction

Share this page

Terence Tao

There are many bits and pieces of folklore in
mathematics that are passed down from advisor to student, or from
collaborator to collaborator, but which are too fuzzy and nonrigorous
to be discussed in the formal literature. Traditionally, it was a
matter of luck and location as to who learned such “folklore
mathematics”. But today, such bits and pieces can be communicated
effectively and efficiently via the semiformal medium of research
blogging. This book grew from such a blog.

The articles, essays, and notes in this book are derived from the
author's mathematical blog in 2010. It contains a broad selection of
mathematical expositions, commentary, and self-contained technical
notes in many areas of mathematics, such as logic, group theory,
analysis, and partial differential equations. The topics range from
the foundations of mathematics to discussions of recent mathematical
breakthroughs.

Lecture notes from the author's courses that appeared on the blog
have been published separately in the Graduate Studies in Mathematics
series.

Readership

Graduate students and research mathematicians interested in
analysis, logic and foundations, PDEs, algebra, and general topics related to
mathematics.

Reviews & Endorsements

Lately, a new generation of
experts, some of whom are very powerful researchers, has started disseminating
exposition via interactive blogs. Since they receive immediate and continuous
international feedback, the interests and needs of their audience inevitably
inform the communication. Tao, who---even among Fields medalists---has
exceptional intellectual range, writes among the most famous of these blogs,
and the present volume contains a selection of redacted content from it.
Whereas many textbooks aim to teach lower-division mathematics majors to
prove trivial theorems, this book explores very generally how research
mathematicians prove nontrivial theorems. But unifying themes aside, Tao has
chosen very well as case studies sundry topics from mutually distant branches
of mathematics. Those sufficiently elementary demand a healthy stretch, and
none will seem overly familiar, even to most experts. The class exhortation
'read the masters' takes on new urgency in an era when the masters return
favor. Highly recommended ... [for] all academic and professional library collections.

There are many bits and pieces of folklore in
mathematics that are passed down from advisor to student, or from
collaborator to collaborator, but which are too fuzzy and nonrigorous
to be discussed in the formal literature. Traditionally, it was a
matter of luck and location as to who learned such “folklore
mathematics”. But today, such bits and pieces can be communicated
effectively and efficiently via the semiformal medium of research
blogging. This book grew from such a blog.

The articles, essays, and notes in this book are derived from the
author's mathematical blog in 2010. It contains a broad selection of
mathematical expositions, commentary, and self-contained technical
notes in many areas of mathematics, such as logic, group theory,
analysis, and partial differential equations. The topics range from
the foundations of mathematics to discussions of recent mathematical
breakthroughs.

Lecture notes from the author's courses that appeared on the blog
have been published separately in the Graduate Studies in Mathematics
series.

Graduate students and research mathematicians interested in
analysis, logic and foundations, PDEs, algebra, and general topics related to
mathematics.

Reviews:

Lately, a new generation of
experts, some of whom are very powerful researchers, has started disseminating
exposition via interactive blogs. Since they receive immediate and continuous
international feedback, the interests and needs of their audience inevitably
inform the communication. Tao, who---even among Fields medalists---has
exceptional intellectual range, writes among the most famous of these blogs,
and the present volume contains a selection of redacted content from it.
Whereas many textbooks aim to teach lower-division mathematics majors to
prove trivial theorems, this book explores very generally how research
mathematicians prove nontrivial theorems. But unifying themes aside, Tao has
chosen very well as case studies sundry topics from mutually distant branches
of mathematics. Those sufficiently elementary demand a healthy stretch, and
none will seem overly familiar, even to most experts. The class exhortation
'read the masters' takes on new urgency in an era when the masters return
favor. Highly recommended ... [for] all academic and professional library collections.